How do I organise and save separate animations in blender?
I think I found what you need. If you go to the animation timeline and change the type to dope sheet, you should see an option next to it that lets you change the type to action editor. This will let you add new actions and save multiple different animations in one rig.
Not entirely sure how you would do it but I think that you may be able to make only certain bones animate for certain actions so if you are running you can have multiple animations only for the arms, and then have variations with holding different guns and shooting as well. Same with the legs too. So you could try and split the rig into those two parts with seperate animations.